Systems, apparatus and methods for quantifying and identifying diversion of electrical energy

ABSTRACT

Systems, apparatus and methods for quantifying and identifying diversion of electrical energy are provided. Bypass and tap diversions may be identified in an electric utility power distribution inventory zone having both bypass and tap diversions. Bypass diversion factors for consumer nodes in an inventory zone are determined by finding a solution to a system of load balance equations having slack variables representing aggregate tap loads for the inventory zone and in which consumer load profile data is scaled by the bypass diversion factors, which solution minimizes an objective function whose value is positively related to the sum of the slack variables representing the aggregate tap loads. Tap loads are correlated with nodes in an inventory zone by solving a first system of power flow equations not having variables representing tap loads, and then solving a second system of power flow equations having variables representing tap loads using an iterative numerical solution technique initialized based on the solution to the first system of power flow equations.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority of U.S. ProvisionalPatent Application No. 61/569,684 filed on Dec. 12, 2011, which isincorporated herein by reference in its entirety.

TECHNICAL FIELD

The invention relates to quantifying and identifying sources ofdiversion of electric energy in electric utility power distributionsystems. Particular embodiments provide method and apparatus foridentifying sources of diversion of electric energy in electric utilitypower distribution systems containing both tap and by-pass diversions.

BACKGROUND

Electric utility energy distribution systems are used to distributeelectric energy from electric power generation plants to electric energyconsumers. FIG. 1 is a schematic diagram of part of an example electricenergy distribution system 10. A high voltage primary distribution line12 provides electric energy to a distribution transformer 14.Distribution transformer 14 is connected to a lower voltage secondarydistribution line 16, and steps down the voltage of primary line 12 tothe voltage of secondary distribution line 16. Secondary distributionline 16 is connected to a plurality of branches 18A, 18B, and 18Ccorresponding to different energy consumers 20A, 20B and 20C. Theconsumption of energy by consumers 20A, 20B and 20C is metered byconsumer meters 22A, 22B and 22C provided on branches 18A, 18B and 18C,respectively.

An unfortunate reality of electric utility energy distribution is thatelectric energy is sometimes unlawfully diverted to avoid metering. Theunlawful diversion of electric energy is sometimes referred to in theelectric energy industry as electricity theft or non-technical losses.Two common forms of electric energy diversion are bypasses and taps.

In FIG. 1, a bypass 24 provides an electrical path in parallel to meter22B, such that a portion of the energy consumed by consumer 20B bypassesmeter 22B so as not to be accounted for in meter 22B's measurement ofelectric energy consumption. Because bypass 24 is connected at eitherside of meter 22B, the amount of electric energy diverted through bypass24 is related to the amount of electric energy delivered through meter22B.

FIG. 1 also shows a distribution tap 26. Distribution tap 26 provides anadditional electrical path from branch 18C to consumer 20C (e.g., to aseparate panel) or to another consumer. Because distribution tap 26 isnot connected on both sides of meter 22C, the amount of electric energydiverted through tap 26 is not related to the amount of electric energydelivered through meter 22C.

Because electric energy diversion is costly to electric energy utilitiesand may be linked to other criminal activity (e.g., clandestinemarijuana grow operations), there is a need for quantifying andidentifying sources of electric energy diversion. It is possible toquantify electric energy diversion within a particular part of anelectric energy distribution network (referred to herein as an“inventory zone”) by comparing the energy delivered to the inventoryzone with metered energy consumption removed from (i.e., consumed in)the inventory zone. In the context of the distribution system 10, theenergy delivered to an inventory zone 28 may be measured by a meter 30connected in series between distribution transformer 14 and secondarydistribution line 16.

If only bypass diversions are present in an inventory zone, it ispossible to identify where bypass diversions are located from the vectork of bypass diversion factors found by measuring energy consumption forthe inventory zone and consumers within the inventory zone for aplurality of intervals, and solving the system of linear equations

$\begin{matrix}{{\begin{bmatrix}w_{11} & \ldots & w_{1j} \\\vdots & \ddots & \vdots \\w_{i\; 1} & \ldots & w_{ij}\end{bmatrix}\begin{bmatrix}k_{1} \\\vdots \\k_{j}\end{bmatrix}} = \begin{bmatrix}w_{z\; 1} \\\vdots \\w_{zi}\end{bmatrix}} & (1)\end{matrix}$

where:

-   -   i is the number of intervals;    -   j is the number of consumers;    -   w_(ij) is the energy consumption measured for the i^(th) time        interval by the meter for the j^(th) consumer, and    -   w_(zi) is the energy consumption measured for the i^(th) time        interval by the distribution transformer meter for the inventory        zone).        -   For convenience, matrix equality (1) may be expressed as            W_(consumer)k=w_(zone) where W_(consumer) is a matrix of            metered consumer load profile data w_(ij) for consumers in            the inventory zone over a number of time intervals (i.e.,            W_(consumer)=[w_(ij)]_(n×m) for m consumers and n time            intervals) and w_(zone) is a vector of inventory zone load            profile data (i.e., w_(zone)=[w_(zi)]_(m)).

This technique fails if the inventory zone contains one or more tapdiversions, since electric energy diverted by way of taps is reflectedin inventory zone load profile w_(zone) but is not reflected in themetered consumer load profiles W_(consumer). Currently, bypassdiversions and tap diversions are identified by manually inspectingelectric power distribution equipment (e.g., transformers, lines,meters, etc.). This is time-consuming and labour intensive.

The inventor has identified a need for methods and apparatus adapted touse metered electric energy consumption data to do one or more of thefollowing:

-   -   quantify bypass diversion loads in an inventory zone that        contains bypass diversions and tap diversions,    -   reliably identify the locations of bypass diversions in an        inventory zone that contains bypass diversions and tap        diversions,    -   quantify tap diversion loads in an inventory zone that contains        bypass diversions and tap diversions, and    -   identify the locations of tap diversions in an electric utility        power distribution system.

The foregoing examples of the related art and limitations relatedthereto are intended to be illustrative and not exclusive. Otherlimitations of the related art will become apparent to those of skill inthe art upon a reading of the specification and a study of the drawings.

SUMMARY

The following embodiments and aspects thereof are described andillustrated in conjunction with systems, tools and methods which aremeant to be exemplary and illustrative, not limiting in scope. Invarious embodiments, one or more of the above-described problems havebeen reduced or eliminated, while other embodiments are directed toother improvements.

An aspect of the invention provides a method for characterizingnon-technical losses in an electric utility power distribution inventoryzone, the inventory zone comprising a plurality of nodes including atleast one metered distribution node and at least two metered consumernodes. In an example embodiment, the method comprises obtaininginventory zone load profile data, obtaining consumer load profile datafor the consumer nodes, and determining bypass diversion factors for theconsumer nodes and aggregate tap loads for the inventory zone that (i)solve a system of load balance equations for the inventory zone havingknown values corresponding to the inventory zone load profile data andto the consumer load profile data and having slack variablesrepresenting the aggregate tap loads, in which the known valuescorresponding to the consumer load profile data are scaled by the bypassdiversion factors and (ii) minimize an objective function whose value ispositively related to the sum of the slack variables representing theaggregate tap loads. In some embodiments, methods according to thisaspect additionally comprise obtaining an admittance matrix modeling theelectrical admittance between the nodes of the inventory zone, obtainingsubstantially simultaneous instantaneous real and reactive load data foreach of the metered nodes of the inventory zone, obtaining substantiallysimultaneous instantaneous voltage magnitude data for each of themetered nodes of the inventory zone, determining a voltage phase anglefor each of the consumer nodes that solve a first system of power flowequations for the inventory zone having known values corresponding tothe real and reactive load data for the consumer nodes and in which thedistribution node is treated as a slack node, and determining real andreactive tap loads corresponding to select ones of the consumer nodesthat (i) solve a second system of power flow equations for the inventoryzone having known values corresponding to the real and reactive loaddata for each of the metered nodes, voltage magnitude valuescorresponding to the voltage data each of the metered nodes, and havingslack variables representing the real and reactive tap loads, and (ii)minimize an objective function whose value is positively related to atleast one of the slack variables representing the real and reactive taploads using an iterative numerical solution technique wherein variablesin the second system of power flow equations corresponding to thevoltage phase angles of the select ones of the consumer nodes areinitialized to values corresponding to the corresponding determinedvoltage phase angles that solve the first system of power flowequations.

Another aspect of the invention provides a method identifying tap loadsin an electric utility power distribution inventory zone, the inventoryzone comprising a plurality of nodes including at least one metereddistribution node and at least metered two consumer nodes. In someembodiments, the method comprises obtaining an admittance matrixmodeling the electrical admittance between the nodes of the inventoryzone, obtaining substantially simultaneous instantaneous real andreactive load data for each of the metered nodes of the inventory zone,obtaining substantially simultaneous instantaneous voltage magnitudedata for each of the metered nodes of the inventory zone, determining avoltage phase angle for each of the consumer nodes that solve a firstsystem of power flow equations for the inventory zone having knownvalues corresponding to the real and reactive load data for the consumernodes and in which the distribution node is treated as a slack node, anddetermining real and reactive tap loads corresponding to select ones ofthe consumer nodes that (i) solve a second system of power flowequations for the inventory zone having known values corresponding tothe real and reactive load data for each of the nodes, voltage magnitudevalues corresponding to the voltage data for each of the metered nodes,and having slack variables representing the real and reactive tap loads,and (ii) minimize an objective function whose value is positivelyrelated to at least one of the slack variables representing the real andreactive tap loads using an iterative numerical solution techniquewherein variables in the second system of power flow equationscorresponding to the voltage phase angles of the select ones of theconsumer nodes are initialized to values corresponding to thecorresponding determined voltage phase angles that solve the firstsystem of power flow equations.

A further aspect of the invention provides a system for characterizingnon-technical losses in an electric utility power distribution inventoryzone, the inventory zone comprising a plurality of nodes including adistribution node and at least two consumer nodes. In some embodiments,the system comprises a data store comprising a non-transitory computerreadable medium containing inventory zone load profile data and consumerload profile data for each of the consumer nodes, and a data processorcommunicatively coupled to the data store. The data processor may beconfigured to obtain the inventory zone load profile data from the datastore, obtain the consumer load profile data for each of the consumernodes from the data store, and determine bypass diversion factors forthe consumer nodes and aggregate tap loads for the inventory zone that(i) solve a system of load balance equations for the inventory zonehaving known values corresponding to the inventory zone load profiledata and to the consumer load profile data and having slack variablesrepresenting the aggregate tap loads, in which the known valuescorresponding to the consumer load profile data are scaled by the bypassdiversion factors, and (ii) minimize an objective function whose valueis positively related to the sum of the slack variables representing theaggregate tap loads. The data processor may be configured to generate arecord in a non-transitory medium indicating the determined bypassdiversion factors and aggregate tap loads.

Yet another aspect of the invention provides a system for identifyingtap loads in an electric utility power distribution inventory zone, theinventory zone comprising a plurality of nodes including at least onemetered distribution node and at least two metered consumer nodes. Insome embodiments, the system comprises a data store comprising anon-transitory computer readable medium of the data store contains anadmittance matrix modeling the electrical admittance between the nodesof the inventory zone, substantially simultaneous instantaneous real andreactive load data for each of the metered nodes of the inventory zone,and substantially simultaneous instantaneous voltage magnitude data foreach of the metered nodes of the inventory zone, and a data processorcommunicatively coupled to the data store. The data processor may beconfigured to obtain the admittance matrix from the data store, obtainthe substantially simultaneous instantaneous real and reactive load datafrom the data store, obtain the substantially simultaneous instantaneousvoltage magnitude data from the data store, determine a voltage phaseangle for each of the consumer nodes that solve a first system of powerflow equations for the inventory zone having known values correspondingto the real and reactive load data for the consumer nodes and in whichthe distribution node is treated as a slack node, and determine real andreactive tap loads corresponding to select ones of the consumer nodesthat (i) solve a second system of power flow equations for the inventoryzone having known values corresponding to the real and reactive loaddata for each of the nodes, voltage magnitude values corresponding tothe voltage data for each of the metered nodes, and having slackvariables representing the real and reactive tap loads, and (ii)minimize an objective function whose value is positively related to atleast one of the slack variables representing the real and reactive taploads using an iterative numerical solution technique wherein variablesin the second system of power flow equations corresponding to thevoltage phase angles of the select ones of the consumer nodes areinitialized to values corresponding to the corresponding determinedvoltage phase angles that solve the first system of power flowequations. The data processor may be configured to generate a record ina non-transitory medium indicating the determined real and reactive taploads corresponding to the select ones of the consumer nodes.

In addition to the exemplary aspects and embodiments described above,further aspects and embodiments will become apparent by reference to thedrawings and by study of the following detailed descriptions.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings show non-limiting example embodiments.

FIG. 1 is a schematic diagram of part of an electric energy distributionsystem 10.

FIG. 2 is a flowchart of a method according to an example embodiment.

FIG. 3 is a flowchart of a method according to an example embodiment.

FIG. 4 is a schematic diagram of an example inventory zone, which isreferred to in describing the example method illustrated by FIG. 3.

FIG. 4A is a schematic diagram of a model of an inventory zonecorresponding to the inventory zone shown in FIG. 4.

FIG. 5 is a flowchart of a method according to an example embodiment.

FIG. 6 is a schematic diagram of a system according to an exampleembodiment.

FIG. 7 is a schematic diagram of another example inventory zone, whichis referred to in describing the example method illustrated by FIG. 8.

FIG. 8 is a flowchart of a method according to an example embodiment.

DETAILED DESCRIPTION

Throughout the following description specific details are set forth inorder to provide a more thorough understanding to persons skilled in theart. However, well known elements may not have been shown or describedin detail to avoid unnecessarily obscuring the disclosure. Accordingly,the description and drawings are to be regarded in an illustrative,rather than a restrictive, sense.

One aspect of the invention provides methods and apparatus fordistinguishing between bypass diversions and tap diversions in aninventory zone. FIG. 2 illustrates a method 40 according to an exampleembodiment. Step 42 comprises obtaining metered inventory zone loadprofile data (e.g., a vector w_(zone)). Step 44 comprises obtainingmetered consumer load profile data for the inventory zone (e.g., amatrix W_(consumer)). Load profile data obtained in steps 42 and 44 maycomprise, for example, time series load measurements obtained at each ofa plurality of meters substantially synchronously (e.g., at consecutiveone hour intervals according to a common clock). Load profile data maybe referred to in the electric power utility industry as “intervaldata”. Steps 42 and 44 may comprise obtaining substantiallysimultaneously acquired load measurements from a network of metersconnected by a wired or wireless network, for example.

Step 46 comprises determining bypass diversion factors k (e.g., eachk_(j) is a multiplier of the value w_(ij) required for the productw_(ij)k_(j) to reflect the j^(th) consumer's metered load and bypassload at the i^(th) time interval) and tap loads s (e.g., each s_(i)represents the total energy in the i^(th) time interval that cannot becorrelated with any consumer's metered consumption) that:

-   -   (1) minimize an objective function whose value is positively        related to the sum of tap loads s (e.g., Z=Σs represents the sum        total energy not attributable to metered consumption or bypass        diversions, which is attributed to tap diversion losses), and    -   (2) solve a system of load balance equations (one equation for        each interval i) in which tap loads s are slack variables:

$\begin{matrix}{{{\begin{bmatrix}w_{11} & \ldots & w_{1j} \\\vdots & \ddots & \vdots \\w_{i\; 1} & \ldots & w_{ij}\end{bmatrix}\begin{bmatrix}k_{1} \\\vdots \\k_{j}\end{bmatrix}} + \begin{bmatrix}s_{1} \\\vdots \\s_{i}\end{bmatrix}} = \begin{bmatrix}w_{z\; 1} \\\vdots \\w_{zi}\end{bmatrix}} & (2)\end{matrix}$

-   -   -   under the constraint k_(j)≧1∀k and s_(i)≧0∀s. For            convenience, the matrix equality (2) may be expressed as            W_(consumer)k+s=w_(zone), where s is a vector of aggregate            tap loads for the inventory zone in each time interval            (i.e., s=[s_(i)]_(m)). Put another way, step 46 comprises            finding bypass diversion factors k and time series aggregate            tap loads s that solve equation (2) and minimize an            objective function whose value is positively related to the            sum of tap loads under the constraints k_(j)≧1∀k and            s_(i)≧0∀s. In some embodiments, the constraint on values in            k is specified to be a value less than one (e.g., k_(j)≧α∀k            where α is a value between 0.95 and 1, such as 0.98 for            example), such as to allow for discrete measurement            resolution, for example.

In some embodiments, the Simplex solution method may be used to obtain asolution for bypass diversion factors k and aggregate tap loads s thatminimizes Z, though other mathematical techniques for minimizing Z canbe used. It may also be possible to use other objective functions for Z.In some embodiments, a Generalized Reduced Gradient solution method, asdescribed below, may be used to obtain a solution for bypass diversionfactors k and aggregate tap loads s that minimizes a non-linearobjective function.

Depending on the magnitude of aggregate tap loads, in some situations itmay be necessary for at least one of the i intervals to have no tapsloads in order to determine bypass diversion factors k. For example, insome situations a large, continuous tap load could be incorrectlyidentified as multiple bypasses. Accordingly, in some embodiments,method 40 may comprise selecting intervals that span a time period thatincludes a tap load transition (e.g., the beginning or end of a tapload). For example, a tap load transition may be identified when thereis a discontinuity in the amount of un-accounted for energy delivered toan inventory zone.

Once bypass diversion factors k are obtained, an element k whose valueis 1 indicates that the j^(th) consumer's meter is not affected by abypass diversion. An element k_(j) whose value is n>1 indicates that thej^(th) consumer's meter is affected by a bypass diversion and that only1/n of the energy consumed by this consumer is registered in the meter(i.e., the remaining (n−1)/n of the energy consumed bypasses the meter).Accordingly, bypass diversion losses in the inventory zone can becomputed for each time interval i as Σ_(j)[w_(ij)(k_(j)−1)].

In some embodiments, method 40 or similar methods may be used todetermine consumer connectivity. For example, in some situations anoperator of electric power utility may be unsure whether or not aparticular consumer is connected to a particular distributiontransformer (e.g. due to incomplete or incorrect records). In such acase, the operator may include that consumer in the inventory zone,modify the constraints such that k_(j)≧0 and the bypass diversion factork for that consumer determined by method 40 will indicate whether or notthat consumer is connected to that distribution transformer, wherein a kvalue of 0 indicates that the user is not connected.

In some situations, certain ones of bypass diversion factors k may havevalues slightly greater than 1 (e.g. 1.1, 1.2, etc.). Such values arelikely the result of numerical artifacts, rather than actual bypasses,as the minimum diversion factor for a typical bypass has a value ofabout 2. Accordingly, in some embodiments additional constraints may beimposed to exclude such results, for example by making the bypassdiversion factors k semi-continuous values. For example, additionalconstraints may be imposed by allowing values equal to 1, or greaterthan or equal to 2 (or, for example, 1.9 or some other typical minimaldiversion factor for the distribution system under study), but not thevalues between 1 and about 2. In such embodiments, by not permittingbypass diversion factors k to have values slightly greater than 1, smallfalse positives may be eliminated, thereby making actual bypasses morereadily identifiable.

Another aspect of the invention provides methods and apparatus foridentifying locations of tap diversions in an inventory zone. FIG. 3illustrates a method 50 for identifying locations of tap diversions inan inventory zone according to an example embodiment. FIG. 4 is aschematic diagram of an example inventory zone 60, which is referred toin describing method 50. In inventory zone 60, distribution transformermeter 62 and consumer meters 64, 66 and 68 measure power distributedfrom a power distribution transformer 70 through an electrical networkof nodes 72, 74, 76 and 78 to consumers 84, 86 and 88. Nodes 72, 74, 76and 78 are respectively associated with distribution transformerdistribution meter 62 and consumer meters 64, 66 and 68. Inventory zone60 includes an unmetered tap load 88A downstream of node 78.

Step 52 comprises obtaining an admittance matrix Y modeling theelectrical admittance between all nodes in the inventory zone. FIG. 4shows electric paths 94, 96 and 98 between node 72 and nodes 74, 76 and78, which paths have admittances Y₁₂, Y₁₃ and Y₁₄ respectively. Paths95, 97 and 99, which have admittances Y₂₃, Y₂₄ and Y₃₄, respectively,are shown notionally in FIG. 4. In the FIG. 4 topology, paths 95, 97 and99 may be zero, but in other topologies may have non-negligible values.In what follows, elements of Y are expressed as G_(ik)+jB_(ik), whereG_(ik) is the magnitude of the real part (also referred to as“conductance”) of the element in the admittance matrix Y at the i^(th)row and k^(th) column and B_(ik) is the magnitude of the imaginary part(also referred to as “susceptance”) of the element in the admittancematrix Y at the i^(th) row and k^(th) column (i.e.,Y=[G_(ik)+jB_(ik)]_(N×N).

Step 54 comprises obtaining substantially simultaneous values for“known” real and reactive loads P_(i) and Q_(i) at all metered nodesN_(i) in the inventory zone (representing energy injected into orremoved from nodes 72, 74, 76 and 78, which may be measured, at least inpart, by meters 62, 64, 66 and 68, respectively). Step 54 may compriseobtaining substantially simultaneous acquired meter values forinstantaneous real and reactive loads at all metered nodes N_(i) in theinventory zone. Where the inventory zone contains bypass diversion(e.g., because a value for k_(i)>1 was determined for at least one nodeN_(i) in method 40), step 54 may comprise scaling the instantaneous realand reactive metered loads at nodes N_(i) affected by bypass diversionsby their corresponding bypass diversion factors k_(i).

Step 56 comprises obtaining substantially simultaneous values for theinstantaneous voltage magnitude |V_(i)| at all metered nodes in theinventory zone, such as might be measured by meters 62, 64, 66 and 68,for example. In some embodiments, step 56 comprises obtainingsubstantially simultaneous values for the instantaneous voltagemagnitude |V_(i)| at less than all metered nodes in the inventory zone.

Step 58 comprises determining complex voltages (magnitude |V_(i)| andangle θ_(i)) for each consumer node by solving an exactly determinedfirst system of real and reactive power flow equations in which thedistribution transformer node is treated as a slack node.

The following two equations are example forms of real and reactive powerflow equations that may be solved for each node N_(i) simultaneously instep 58:

$\begin{matrix}{0 = {{- P_{i}} + {\sum\limits_{k = 1}^{N}\; {{V_{i}}{V_{k}}\left( {{G_{ik}{\cos \left( {\theta_{i} - \theta_{k}} \right)}} + {B_{ik}{\sin \left( {\theta_{i} - \theta_{k}} \right)}}} \right)}}}} & (3) \\{0 = {{- Q_{i}} + {\sum\limits_{k = 1}^{N}\; {{V_{i}}{V_{k}}\left( {{G_{ik}{\sin \left( {\theta_{i} - \theta_{k}} \right)}} - {B_{ik}{\cos \left( {\theta_{i} - \theta_{k}} \right)}}} \right)}}}} & (4)\end{matrix}$

In equations (3) and (4):

-   -   P_(i) is the real load at node N_(i) and        -   where node N_(i) is one of consumer nodes 74, 76 and 78,            P_(i) has the value obtained in step 54, and        -   where node N_(i) is the distribution transformer node 72,            P_(i) is treated as unknown;    -   Q_(i) is the reactive load at node N_(i) and        -   where node N_(i) is one of consumer nodes 74, 76 and 78,            Q_(i) has the value obtained in step 54, and        -   where node N_(i) is the distribution transformer node 72,            Q_(i) is treated as unknown;    -   |V_(i)| is the voltage magnitude at node N_(i) and        -   where node N_(i) is one of consumer nodes 74, 76 and 78,            |V_(i)| is treated as unknown; N_(i) may be initialized to            an arbitrary value (e.g., a nominal system voltage for a            “flat start”) or to a value obtained in step 56 (e.g., for            distribution transformer node 72, for node N_(i) or for            another consumer node);        -   where node N_(i) is distribution transformer node 72,            |V_(i)| has the value obtained in step 56 for distribution            transformer node 72;    -   G_(ik) is the real part of the element at the i^(th) row and        k^(th) column in the admittance matrix Y determined in step 52;    -   B_(ik) is the imaginary part of the element at the i^(th) row        and k^(th) column in the admittance matrix Y determined in step        52;    -   θ_(i) is the voltage phase angle at node N_(i) and        -   where node N_(i) is one of consumer nodes 74, 76 and 78,            θ_(i) is treated as unknown and initialized to an arbitrary            value (e.g., zero for a “flat start”), and        -   where node N_(i) is distribution transformer node 72, θ_(i)            is fixed arbitrarily at an arbitrary value (e.g., the same            value as the initial value of θ_(i) for consumer nodes, such            as zero for a “flat start”).

The solution obtained to the system of real and reactive power flowequations represents the power flow solution for “known” consumer loads,and is used as the starting point for finding tap theft locations instep 59. Numerical methods, such as the Newton-Raphson and GeneralizedReduced Gradient methods, for example, may be used to solve the powerflow equations to obtain complex voltages for consumer nodes. It will beappreciated that though a system of equations having equations in theform of equations (3) and (4) for each node in an inventory zone has thesame number of equations as it does unknowns, the initial approximationsof the unknowns may affect whether numerical methods converge to thesolution of the system.

Step 59 comprises determining real tap loads P_(i) ^(T) and/or reactivetap loads Q_(i) ^(T) corresponding to one or more nodes N_(i) that:

-   (1) minimize an objective function Z whose value is positively    related to the sum total of the magnitudes of the determined real    and reactive tap loads

(e.g., Z=√{square root over (Σ_(i=1) ^(N)(P _(i) ² +Q _(i) ²))}), and

-   (2) solve a second system of real and reactive power flow balance    equations in which tap affected voltage phase angles θ_(i) ^(T) at    consumer nodes are unknown variables and the real tap loads P_(i)    ^(T) and/or reactive tap loads Q_(i) ^(T) are slack variables.

Put another way, step 59 comprises finding consumer node voltage phaseangles θ_(i) ^(T) and one or more real and reactive tap loads P_(i) ^(T)and Q_(i) ^(T) corresponding to one or more nodes N_(i) that solve asecond system of real and reactive power flow balance equations in whichthe real and reactive tap loads are slack variables and minimize anobjective function whose value is positively related to the apparentpower of the determined tap loads (i.e., the square root of the sum ofthe squares of the determined real and reactive tap loads). Real andreactive tap loads P_(i) ^(T) and Q_(i) ^(T) may be determined in step59 by using a numerical method in which the variables for tap affectedvoltage phase angle θ_(i) ^(T) at consumer nodes are initialized to thevalue θ_(i) determined in step 58.

The following two equations are example forms of real and reactive powerflow equations that may be solved in step 59:

$\begin{matrix}{0 = {{- P_{i}^{T}} - P_{i} + {\sum\limits_{k = 1}^{N}\; {{V_{i}}{V_{k}}\left( {{G_{ik}{\cos \left( {\theta_{i}^{T} - \theta_{k}^{T}} \right)}} + {B_{ik}{\sin \left( {\theta_{i}^{T} - \theta_{k}^{T}} \right)}}} \right)}}}} & (5) \\{0 = {{- Q_{i}^{T}} - Q_{i} + {\sum\limits_{k = 1}^{N}\; {{V_{i}}{V_{k}}\left( {{G_{ik}{\sin \left( {\theta_{i}^{T} - \theta_{k}^{T}} \right)}} - {B_{ik}{\cos \left( {\theta_{i}^{T} - \theta_{k}^{T}} \right)}}} \right)}}}} & (6)\end{matrix}$

In equations (5) and (6):

-   -   P_(i)T is the unknown real tap load at node N_(i), and is        initialized to zero;    -   Q_(i) ^(T) is the unknown reactive tap load at node N_(i), and        is initialized to zero;    -   P_(i) is the known real load at node N_(i) obtained in step 54;    -   Q_(i) is the known reactive load at node N_(i) obtained in step        54;    -   |V_(i)| is the measured voltage magnitude at node N_(i) obtained        in step 56;    -   G_(ik) is the real part of the element at the i^(th) row and        k^(th) column in the admittance matrix Y determined in step 52;    -   B_(ik) is the imaginary part of the element at the i^(th) row        and k^(th) column in the admittance matrix Y determined in step        52;    -   θ_(i) ^(T) is the unknown tap affected voltage phase angle at        node N_(i) and        -   where node N_(i) is a consumer node, θ_(i) ^(T) is            initialized to the value of θ_(i) determined in step 58, and        -   where node N_(i) is the distribution transformer node, θ_(i)            ^(T) is fixed at the same value it was fixed at in step 58            (e.g., to zero).

In some cases, the initialization of θ_(i) ^(T) in step 59 to the valueof θ_(i) determined in step 58 may promote convergence of theoptimization of the second system of equations to a solution that placesthe tap theft loads P_(i) ^(T) and Q_(i) ^(T) at the correct nodes.

The solution obtained in step 59 represents the power flow solution forthe “known” consumer loads, measured consumer voltage magnitudes and thesolution set of tap affected node voltage angles of θ_(i) ^(T), and thesolution set of P_(i) ^(T) and Q_(i) ^(T) tap theft loads values. Nodeshaving relatively larger values of P_(i) ^(T) (and/or Q_(i) ^(T)) arerelatively more likely to be affected by tap diversions. Nodes havingvalues of P_(i) ^(T) that are zero or relatively close to zero are morelikely to not be affected by tap diversions.

There may be cases where the step 59 optimization does not converge to avalid solution. In some embodiments, one or more additional constraintsmay be added to the system of equations that constrains the step 59optimization to promote convergence to a valid solution. For example, insome embodiments equations specifying a relationship between thevariables P_(i) ^(T) and Q_(i) ^(T) for one or more nodes N_(i) havingthese variables in their corresponding power flow equations are added toa system of real and reactive power flow equations that constrains thestep 59 optimization. For example, a linearly proportional relationshipbetween P_(i) ^(T) and Q_(i) ^(T) may be specified, such in the formQ_(i) ^(T)=a P_(i) ^(T) to further constrain the step 59 optimization.In a non-limiting example embodiment, a is specified as 0.2.

A specified relationship between P_(i) ^(T) and Q_(i) ^(T) may reflectan estimated or expected power factor of the possible tap load at thenode. For instance, where PF_(i) denotes the expected or estimated powerfactor of a possible tap load at node N_(i), equations in the form

$\begin{matrix}{Q_{i}^{T} = {P_{i}^{T}\sqrt{\frac{\left( {1 - {PF}_{i}^{2}} \right)}{{PF}_{i}^{2}}}}} & (7)\end{matrix}$

may be added to a system of real and reactive power flow equations thatconstrains the step 59 optimization. PF_(i) may be the same or differentamong nodes in an inventory zone. In some embodiments, power factorPF_(i) for possible tap loads may be estimated based on a differencebetween values for P_(i) and Q_(i) determined for the distribution nodein step 58 and values for real and reactive power measured for thedistribution node in step 54. The difference between the power valuesdetermined in step 58 and the power values measured in step 54 reflectsthe aggregate tap load, and a power factor determined from the real andreactive power differences reflects the power factor of the aggregatetap load. This power factor may be used as an estimate of the powerfactor PF_(i) of the individual possible tap loads, and accordingly usedto relate P_(i) ^(T) and Q_(i) ^(T) to further constrain the secondsystem of power flow equations solved in step 59. In some embodiments, apower factor for tap loads is specified based on expectations derivedfrom past experience (e.g., power factor of tap loads previouslydetected in that inventory zone or other inventory zones).

In some embodiments, the step 59 power flow equations for one or morenodes do not include one or both of variables P_(i) ^(T) and Q_(i) ^(T).For example, variables P_(i) ^(T) and Q_(i) ^(T) may not be included inthe power flow equation for a node (e.g., the distribution transformernode) when there is confidence that there is no tap diversion proximateto the node. For another example, Q_(i) ^(T) may not be included in thepower flow equation for a node when there is confidence that any tapdiversion that might be present at the node does not have an appreciablereactive component. Omitting variables P_(i) ^(T) and/or Q_(i) ^(T) fromone or more power flow equations reduces the number of unknown variablesto be determined in the step 59 optimization, and may promoteconvergence of the step 59 optimization to a valid solution. In somecases, not including one or both of variables P_(i) ^(T) and Q_(i) ^(T)in the step 59 power flow equation for a node that is in fact affectedby a tap diversion may result in method 50 allocating the tap diversionamong nearby nodes. Where this occurs, the number of tap diversionsindicated by the result of method 50 may appear to be unusually large.Variables P_(i) ^(T) and Q_(i) ^(T) may be added to the power flowequation of a node for which they were previously omitted that isproximate to a “cluster” of tap diversions indicated by the result, andmethod 50 performed again with the “new” P_(i) ^(T) and Q_(i) ^(T)variables.

In some cases it may be necessary or convenient to include unmeterednodes in applications of method 50. For example, an electric powerutility's admittance model for a distribution network in an inventoryzone may comprise unmetered nodes (e.g., in order to correspond with thephysical topology of the inventory zone). FIG. 4A shows an example model100 that corresponds to inventory zone 60 shown in FIG. 4. In model 100,metered nodes 74, 76 and 78 are connected to corresponding unmeteredintermediate nodes 74A, 76A and 78A. Nodes 74A, 76A and 78A areconnected in series to node 72. Power delivered to node 72 is metered bymeter 62.

Nodes 74A, 76A and 78A may be included in method 50 as follows.

-   -   The admittance matrix obtained in step 52 may contain elements        corresponding to paths between nodes 74A, 76A and 78A and the        other nodes in the inventory zone.    -   Since nodes 74A, 76A and 78A are unmetered, no measurements are        obtained for them in steps 54 and 56.    -   In step 58, equations corresponding to nodes 74A, 76A and 78A        are included in the first system of power flow equations. In        these equations, voltage magnitude |Vi| and phase angle θ_(i)        are both treated as unknowns, and the real and reactive power        terms P_(i) and Q_(i) are fixed at arbitrary values (e.g., zero        or another small value corresponding to expected technical loss,        known unmetered load, etc. at the nodes).    -   In step 59, equations corresponding to nodes 74A, 76A and 78A        are included in the second system of power flow equations. In        these equations, voltage magnitude |Vi| and tap affected phase        angle θ_(i) ^(T) are treated as unknowns. Where the second        system of equations is solved using an iterative numerical        technique, these unknowns may be initialized to the        corresponding values calculated for voltage magnitude |Vi| and        phase angle θ_(i) in step 58. These equations may not include        real and reactive tap power terms P_(i) ^(T) and Q_(i) ^(T),        since in some cases this could prevent solution of the second        system of equations. If it occurs that one or more of nodes 74A,        76A and 78A is in fact affected by a tap diversion, method 50        may allocate the tap diversion among nearby metered nodes. Where        the result of step 59 indicates that one or more of nodes 74A,        76A and 78A is surrounded by a “cluster” of tap diversions,        variables P_(i) ^(T) and Q_(i) ^(T) may be added to the power        flow equations for those one or more of nodes 74A, 76A and 78A,        and removed from the power flow equations for nearby metered        nodes. Step 59 may then be performed again with the “new” P_(i)        ^(T) and Q_(i) ^(T) variables for the one or more unmetered        nodes.

Information quantifying and identifying bypass and tap diversions inelectric utility networks obtained by practice of methods of theinvention (e.g., methods 40 and/or 50), may be used in the automaticcontrol of electric utility networks and billing of customers of suchnetworks. FIG. 5 is a flow chart of a method 120 according to an exampleembodiment. In method 120, step 122 comprises determining whether thereis at least one bypass diversion present in an inventory zone based onload profile data 124 for the inventory zone. Step 122 may comprise oneor more steps of method 40, for example. In some embodiments, step 122comprises whether any node of the inventory zone has a bypass diversionfactor determined in step 46 greater than a threshold (e.g., one, anumber greater than one).

If in step 122 it is determined that there is at least one bypassdiversion in the inventory zone (step 122, YES), method 122 proceeds tostep 126. Step 126 comprises identifying the nodes affected by bypassdiversion(s) in the inventory zone. In embodiments where step 122comprises determining a set of bypass diversion factors, as is done inmethod 40, for example, step 126 may comprise determining which nodeshave bypass diversion factors greater than 1, for example. After step126, method 120 may proceed to either of both of steps 128 and 130. Step128 comprises cutting power to the bypass-affected nodes identified instep 126. Step 130 comprises scaling load profile data for thebypass-affected nodes identified in step 126. This bypass-scaled loaddata may be used for billing customers for bypass loads in step 132. Itwill be appreciated that steps 122 through 132 may be automated (e.g.,performed without human intervention). It will also be appreciated thatnodes identified as being affected by bypass diversion(s) in step 126 bemanually inspected prior to performing one or both of steps 128 and 130.

If in step 122 it is determined that there is not at least one bypassdiversion in the inventory zone (step 122, NO), method 122 proceeds tostep 138.

Step 126 is also followed by step 134. Both step 134 and 138 comprisedetermining whether there is one or more tap diversions in the inventoryzone. Step 134 and/or step 138 may comprise one or more steps of method40 for example. In some embodiments, one or both of steps 134 and 138comprises determining whether any tap diversion loads determined in step46 of method 40 are non-zero.

If in step 134 or step 138 it is determined that there is not one ormore tap diversions in the inventory zone (step 134 or step 138, NO),method 120 proceed to termination 136.

If in step 134 it is determined that there is one or more tap diversionsin the inventory zone (step 134, YES), method 120 proceeds to step 140.Step 140 comprises scaling instantaneous load data 142 forbypass-affected nodes identified in step 126. Step 140 may comprisescaling instantaneous load data for a bypass-affected node by a bypassdiversion factor determined in step 46 of method 40, for example. Afterstep 140, method 120 proceeds to step 144.

If in step 138 it is determined that there is one or more tap diversionsin the inventory zone (step 138, YES), method 120 proceeds to step 144.Step 144 comprises identifying nodes affected by tap diversion based oninstantaneous load and voltage data. Step 144 may comprise one or moresteps of method 50, for example. In some embodiments, step 144 comprisesidentifying nodes determined to have real and/or reactive tap loadvalues (P_(i) ^(T) and Q_(i) ^(T)) determined in step 59 of method 50greater than a threshold (e.g., in some embodiments, the threshold maybe zero, or a number greater than zero).

After step 144, method 120 may proceed to either of both of steps 146and 148. Step 146 comprises cutting power to the tap-affected nodesidentified in step 144. Step 148 comprises determining tap loads for thetap-affected nodes identified in step 144. Step 144 may comprisedetermining for real and/or reactive tap load values (P_(i) ^(T) andQ_(i) ^(T)), as in step 59 of method 50, for example. Tap loadsdetermined in step 148 may be used for billing customers for tap loadsin step 150. In some embodiments, customers at tap-affected nodes arebilled for energy consumption calculated based on the determined taploads for their nodes and estimated time period in which their tap loadswere active (such as may be inferred by analyzing changes in thedifference between a metered load or consumption for the inventory zoneand the sum of metered load or consumption for consumer nodes in theinventory zone). It will be appreciated that steps 122 through 150 maybe automated (e.g., performed without human intervention). It will alsobe appreciated that nodes identified as being affected by tapdiversion(s) in step 144 be manually inspected prior to performing oneor both of steps 146 and 150.

FIG. 6 is a schematic diagram of a system 200 according to an exampleembodiment. System 200 comprises a plurality of electric energy meters202. Meters 202 are configured to obtain at least load profile data, andmay be configured to obtain instantaneous real and reactive power dataand instantaneous voltage data. Meters 202 include a plurality ofconsumer meters and at least one upstream meter (e.g., a distributiontransformer meter) that meters energy delivered to a subset of at leasttwo of the consumer meters (e.g., an inventory zone). Meters 202 arecommunicatively coupled to a hub 204. In the illustrated system, meters202 are wireless networked with hub 204, but this is not necessary.Meters 202 may be communicatively coupled with each other (e.g., in amesh network), or may have direct links to hub 204, for example. Hub 204is configured to aggregate data obtained by meters 202.

Hub 204 is communicatively coupled via a communication network 206 to adata processor 208. Network 206 may comprise a public network (e.g., theInternet) or a private network (e.g., comprised of private communicationlinks), and may be implemented using any suitable networking technology(e.g., packet based, switched link, etc.).

Data processor 208 may comprise one or more central processing units(CPUs), one or more microprocessors, one or more field programmable gatearrays (FPGAs), application specific integrated circuits, logiccircuits, or any combination thereof, or any other suitable processingunit(s) comprising hardware and/or software capable of functioning asdescribed herein. Data processor 208 is coupled to a data store 210.Data store 210 comprises one or more non-transitory computer readablemedia. Data processor 208 is configured to store data obtained by meters202 and received at data processor 208 (e.g., via hub 204 and network206) in data store 210.

Data processor 208 is also configured to execute one or more steps ofmethods 40, 50 and 120. For example, data processor may be configured toexecute software instructions contained in a non-transitorycomputer-readable medium of data store 210, which instructions whenexecuted by data processor 208 cause data processor 208 to perform oneof more steps of methods 40, 50 and 120. Data processor 208 may beconfigured to cause output of methods 40, 50 and/or 120 (e.g.,identification of nodes affected by tap diversions and/or bypassdiversions, bypass loads and/or tap loads associated with nodes,customer billing information, etc.) to be displayed on a display 212, toprinted on print media 214 by a printer 216, and/or to be stored as arecord in non-transitory computer-readable media of data store 210, forexample.

Data processor 208 may comprise physically remote and independentlyoperating components, one of which stores data obtained by meters 202 indata store 210 and another that performs steps of methods 40, 50 and/or120. Data store 210 may comprise physically remote and independentlyoperating components, one of which stores data obtained by meters 202and another that stores computer-readable instructions executable bydata processor 208.

In some situations, it may be problematic to properly identify thelocations of tap diversions in an inventory zone due to voltagemeasurement errors. For example, certain currently available consumermeters have a rated measurement error of about 0.5%. Some types ofmeters have typical measurement errors of about 0.2%. Accordingly, it ispossible that in some circumstances method 50 described above may failto converge on a solution. In such circumstances, a modified method maybe performed to locate tap diversions wherein a “secondary tap” at oneof a plurality of distribution nodes is considered, as discussed belowwith reference to FIGS. 7 and 8.

FIG. 7 shows an example inventory zone 300 wherein a distributiontransformer 302 supplies sixteen consumers 320A-P. The total powerdelivered to inventory zone 300 by distribution transformer 302 ismetered by a distribution meter 304. The power delivered to each ofconsumers 320A-P (other than any power which is unlawfully diverted) isrespectively metered by consumer meters 322A-P. Consumers 320A-P arearranged into four groups connected (through their respective meters) toa secondary distribution line 310 at four separate distribution nodes312, 314, 316, 318, with consumers 320A-D connected to node 312,consumers 320E-H connected to node 314, consumers 3201-L connected tonode 316, and consumers 320M-P connected to node 318. Distributiontransformer 302 is also connected (through distribution meter 304) tonode 316.

FIG. 8 illustrates an example method 400 for identifying locations oftap diversions in an inventory zone. Method 400 is described withreference to example inventory zone 300 of FIG. 7, but it is to beunderstood that method 400 could be useful for identifying locations oftap diversions in any inventory zone with two or more distributionnodes. Method 400 may, for example, be performed wholly or in part byone or more processing elements, such as for example data processor 208.

Step 402 comprises determining tap loads at consumer nodes using themeasured loads and voltages at the consumer nodes. Step 402 may compriseone or more steps of method 50, for example. If a solution is reached atstep 404, method 400 proceeds to end at step 406. If a solution is notreached at step 404, method 400 proceeds to step 408. A solution may notbe reached, for example, if the determination at step 402 fails toconverge (e.g., the error terms are not less than a predeterminedconvergence threshold). However, even if the determination at step 402fails to converge, it will identify consumers where tap diversions arelikely. Accordingly, the results of the determination at step 402 areused in step 408.

In step 408 a set of secondary tap power flow equations are generatedwhich allow for a tap at one of the secondary distribution nodes byassigning the real and reactive tap loads and the voltage magnitude andphase at the secondary distribution node as unknown variables todetermine. The consumer tap loads are fixed to the values determined instep 402, and the consumer voltage magnitudes and phases are alsounknown variables to determine. The secondary tap power flow equationsmay have the same general form as equations (5) and (6) above. Forexample, in some embodiments step 408 may comprise taking the resultsfrom step 402 and changing which values are fixed and which values arevariable to generate the secondary tap power flow equations.

In step 410, real and reactive tap loads and the voltage magnitude andphase at the secondary distribution node under consideration, as well asconsumer voltage magnitudes and phases, that satisfy the secondary tappower flow equations are numerically determined (e.g., by a GeneralizedReduced Gradient method as discussed above). If a solution is reached atstep 412 (e.g. the solution converges), method 400 proceeds to step 414and the calculated consumer voltage magnitudes are stored in a tableindexed by the secondary distribution node (or another suitable datastructure). Step 414 may also comprise storing complex consumervoltages, consumer tap magnitudes and/or secondary tap magnitudes. Forexample, consumer and secondary tap magnitudes may optionally be used tovalidate the results of method 400 by comparing the total loss measuredfor inventory zone 300 to the sum of the taps calculated by method 400(with appropriate adjustments for any bypasses, as discussed above). Ifa solution is not reached at step 412, method 400 bypasses step 414(such that the voltages are not stored) and proceeds to step 416.

At step 416, if the secondary distribution node under consideration isnot the last distribution node (i.e., if all secondary distributionnodes have not yet been considered), method 400 proceeds to step 418where a next distribution node is considered. After step 418, method 400repeats steps 408 to 416 until the last distribution node has beenconsidered.

After all of the distribution nodes have been considered (step 416,YES), method 400 proceeds to step 420, where differences between themeasured voltages and the calculated consumer voltage magnitudes storedin step 414 are determined for each distribution node. At step 422, anyvoltage difference that exceeds the respective meter's rated measurementerror is identified as a voltage violation. At step 424, a voltagedifference range is calculated for each distribution node by determiningthe “spread” in voltage differences. In other words, the voltagedifference range for a distribution node is the range between thehighest positive voltage difference determined in step 420 and thelowest negative voltage difference determined in step 420.

At step 426, the secondary distribution node(s) having the smallestvoltage difference range (in no case more than twice the meters' ratedmeasurement error) and the fewest voltage violations determined at step422 is determined to be a likely location of a secondary distributionsystem tap. If one of the secondary distribution nodes has a voltagedifference range of less than twice the meters' rated measurement error,or has a significantly lower voltage difference range than the othersecondary distribution nodes, then that secondary distribution node isdetermined to be the most likely location of a secondary tap. In somesituations, more than one secondary distribution node may be determinedto be a likely tap location. For example, with reference to FIG. 3, inthe situation of a secondary tap on distribution line 310 between nodes312 and 314, the voltage difference ranges and number of voltageviolations calculated for nodes 312 and 314 may be similar. In order tomore precisely determine the likely location of the secondary tap, insome embodiments step 426 comprises determining and comparing cumulativevoltage differences between the measured voltages and calculatedvoltages for each secondary distribution node stored in step 414. Thecumulative voltage difference for each secondary distribution node isthe sum of the differences between the measured consumer voltages andthe consumer voltages calculated when allowing for a tap at that node.In one example, when a secondary tap is between secondary distributionnodes 312 and 314, the cumulative voltage difference when allowing for atap at node 312 indicates that the calculated voltages tend to be lowerthan the measured voltages, and the cumulative voltage difference whenallowing for a tap at node 314 indicates that the calculated voltagestend to be higher than the measured voltages, and the ratio ofcumulative voltage differences (or another suitable relationship betweenthe voltage differences when allowing for a tap a node 312 and thevoltage differences when allowing for a tap at node 314) may be used todetermine the most likely location of a secondary tap along distributionline 310 between nodes 312 and 314.

The location of the secondary tap determined at step 426 may be outputby any suitable means, including those described above with respect tosystem 200 of FIG. 6. After step 426, method 400 ends at step 428.

It will be appreciated from the foregoing that determining the presenceand identifying the locations of bypass and tap diversions is anundertaking whose complexity expands dramatically with the number ofnodes in an inventory zone. For inventory zones of even a few meters,the numerical solution methods required to perform the methods disclosedherein cannot, as a practical matter, be performed entirely in a human'smind and accordingly requires use of a machine configured to performsuch methods.

Where a component or feature is referred to above (e.g., meter,transformer, inventory zone, load profile data, interval data, dataprocessor, data store, hub, printer, display, etc.), unless otherwiseindicated, reference to that component (including a reference to a“means”) should be interpreted as including as equivalents of thatcomponent any component which performs the function of the describedcomponent (i.e., that is functionally equivalent), including componentswhich are not structurally equivalent to the disclosed structure whichperforms the function in the illustrated exemplary embodiments of theinvention.

Unless the context clearly requires otherwise, throughout thedescription and the claims, the words “comprise,” “comprising,” and thelike are to be construed in an inclusive sense, as opposed to anexclusive or exhaustive sense; that is to say, in the sense of“including, but not limited to.” Where the context permits, words in theabove description using the singular or plural number may also includethe plural or singular number respectively. The word “or,” in referenceto a list of two or more items, covers all of the followinginterpretations of the word: any of the items in the list, all of theitems in the list, and any combination of the items in the list.

The above detailed description of example embodiments is not intended tobe exhaustive or to limit this disclosure and claims to the preciseforms disclosed above. Those skilled in the art will appreciate thatcertain features of embodiments described herein may be used incombination with features of other embodiments described herein, andthat embodiments described herein may be practiced or implementedwithout all of the features ascribed to them herein, as would beapparent to the skilled addressee. While specific examples of, andexamples for, embodiments are described above for illustrative purposes,various equivalent modifications are possible within the scope of thetechnology, including variations comprising mixing and matching offeatures from different embodiments, as those skilled in the relevantart will recognize.

These and other changes can be made to the system in light of the abovedescription. While the above description describes certain examples ofthe technology, and describes the best mode currently contemplated, nomatter how detailed the above appears in text, the technology can bepracticed in many ways. As noted above, particular terminology used whendescribing certain features or aspects of the system should not be takento imply that the terminology is being redefined herein to be restrictedto any specific characteristics, features, or aspects of the system withwhich that terminology is associated. In general, the terms used in thefollowing claims should not be construed to limit the system to thespecific examples disclosed in the specification, unless the abovedescription section explicitly and restrictively defines such terms.Accordingly, the actual scope of the technology encompasses not only thedisclosed examples, but also all equivalent ways of practicing orimplementing the technology under the claims.

As will be apparent to those skilled in the art in light of theforegoing disclosure, many alterations and modifications are possible tothe methods and systems described herein. For example:

-   -   Methods described herein may be applied to electric distribution        systems having topologies different from those of the example        systems shown herein.    -   Inventory zones may be defined between feeder meters. For one        example, the difference between metered readings of upstream and        downstream feeder meters may be treated as readings for an        inventory zone that draws electric energy from between the        feeder meters. For another example, a meter reading of an        upstream feeder meter may be treated as a reading for an        inventory zone, and a downstream feeder meter treated as a        consumer node in the inventory zone. An inventory zone defined        between by feeder meters may comprise a plurality of        transformers, each of which supplies electric energy to a        plurality of consumer nodes.    -   Measured load profile and energy consumption data (e.g.,        obtained from meters) may be pre-conditioned prior to being used        in methods described herein. For example, data may be modified        to eliminate anomalies revealed by simple inspection of data,        such as meter inversions and meter removals.    -   Distribution taps may be identified or accounted by inserting        dummy nodes having no “known” (e.g., metered) load or        consumption at appropriate locations in a network topology, and        performing methods described herein on the topology including        the dummy nodes.    -   Methods and techniques described herein may be modified to        account for technical losses. A non-limiting example of such a        modification can be posited for the case where feeder meters are        used to determine energy consumption for an inventory zone is        located close to a head-end substation. In this case, the        load(s) downstream from the inventory zone may be large enough        to cause non-trivial technical losses inside the inventory zone,        which could be mistaken for non-technical losses (e.g., theft).        A dummy load equal the expected technical losses (e.g., as        calculated based on downstream load and distribution line        impedance) may be added to the inventory zone to account for the        technical losses.    -   Methods and techniques described herein may be adapted for use        with distribution of fluid commodities by analogizing properties        of electric energy distribution to properties of fluids. For        example, some methods and techniques described herein may be        adapted to detect water and natural gas theft by analogizing        consumption to volume, load to flow and voltage to pressure.

While a number of exemplary aspects and embodiments have been discussedabove, those of skill in the art will recognize certain modifications,permutations, additions and sub-combinations thereof. It is thereforeintended that the following appended claims and claims hereafterintroduced are interpreted to include all such modifications,permutations, additions and sub-combinations as are may reasonably beinferred by one skilled in the art. The scope of the claims should notbe limited by the embodiments set forth in the examples, but should begiven the broadest interpretation consistent with the foregoingdisclosure.

What is claimed is:
 1. A method for identifying tap loads in an electricutility power distribution inventory zone, the inventory zone comprisinga plurality of nodes including a metered distribution node and at leasttwo metered consumer nodes, the method comprising: obtaining anadmittance matrix modeling the electrical admittance between the nodesof the inventory zone; obtaining substantially simultaneousinstantaneous real and reactive load data for each of the metered nodesof the inventory zone; obtaining substantially simultaneousinstantaneous voltage magnitude data for each of the metered nodes ofthe inventory zone; determining a voltage phase angle for each of theconsumer nodes that solve a first system of power flow equations for theinventory zone having known values corresponding to the real andreactive load data for the consumer nodes and in which the distributionnode is treated as a slack node; and determining real and reactive taploads corresponding to select ones of the consumer nodes that: solve asecond system of power flow equations for the inventory zone havingknown values corresponding to the real and reactive load data for eachof the nodes, voltage magnitude values corresponding to the voltage datafor each of the metered nodes, and having slack variables representingthe real and reactive tap loads, and minimize an objective functionwhose value is positively related to at least one of the slack variablesrepresenting the real and reactive tap loads using an iterativenumerical solution technique wherein variables in the second system ofpower flow equations corresponding to the voltage phase angles of theselect ones of the consumer nodes are initialized to valuescorresponding to the corresponding determined voltage phase angles thatsolve the first system of power flow equations.
 2. The method of claim 1wherein the select ones of the consumer nodes comprise all of theconsumer nodes in the inventory zone.
 3. The method of claim 1 whereinat least one of the consumer nodes in the inventory zone is not one ofthe select ones of the consumer nodes.
 4. The method of claim 1 whereinin the first system of power flow equations variables corresponding tothe voltage magnitudes of the consumer nodes are initialized to valuescorresponding to the instantaneous voltage magnitude data obtained forthe distribution node.
 5. The method of claim 4 wherein in the firstsystem of power flow equations a term corresponding to a voltagemagnitude of the distribution node is fixed to equal a valuecorresponding to the instantaneous voltage magnitude data obtained forthe distribution node.
 6. The method of claim 5 wherein in the firstsystem of power flow equations a term corresponding to a voltage phaseangle of the distribution node is fixed to equal zero.
 7. The method ofclaim 6 wherein in the second system of power flow equations a termcorresponding to a voltage phase angle of the distribution node is fixedto equal zero.
 8. The method of claim 1 wherein in the second system ofpower flow equations variables corresponding to the real and reactivetap loads of a consumer node are further constrained by a pre-determinedrelationship with one another.
 9. The method of claim 8 wherein thepre-determined relationship comprises a linear relationship.
 10. Themethod of claim 8 wherein the pre-determined relationship specifies thatthe reactive tap load is equal to the product of the real tap load and ascale factor.
 11. The method of claim 10 wherein the scale factor isless than or equal to 0.2.
 12. The method of claim 10 comprisingdetermining the scale factor by: determining a real component ofaggregate tap power based on a difference between a real power value forthe distribution node that solves the first system of power flowequations and a real power value for the distribution node correspondingto the obtained instantaneous real load data for the distribution node;determining a reactive component of aggregate tap power based on adifference between a reactive power value for the distribution node thatsolves the first system of power flow equations and a reactive powervalue for the distribution node corresponding to the obtainedinstantaneous reactive load data for the distribution node; anddetermining the scale factor as an aggregate tap power factor based onthe real and reactive components of aggregate tap power.
 13. The methodof claim 1 wherein the inventory zone comprises one or more unmeterednodes, and wherein in the first system of power flow equations voltagemagnitude and phase angles for the unmetered nodes are treated asunknowns and wherein real and reactive power for the unmetered nodes arefixed to arbitrary values.
 14. The method of claim 13 wherein in thesecond system of power flow equations voltage magnitude and tap affectedphase angles for the unmetered nodes are treated as unknowns.
 15. Themethod of claim 1 wherein the inventory zone comprises two or moresecondary distribution nodes to which metered consumer nodes areconnected, comprising, when the iterative numerical solution techniquefails to converge: for each secondary distribution node: determiningcalculated complex consumer voltages and real and reactive secondary taploads corresponding to that secondary node that solve a third system ofpower flow equations for the inventory zone which allow for a secondarytap at that secondary distribution node having fixed valuescorresponding to the real and reactive tap loads determined for theconsumer nodes, and having slack variables representing calculatedconsumer voltages and real and reactive secondary tap loads, andminimize an objective function whose value is positively related to atleast one of the slack variables representing the calculated consumervoltages and real and reactive secondary tap loads using an iterativenumerical solution technique; and, when the iterative numerical solutiontechnique converges to a solution, storing calculated voltage magnitudescorresponding to the calculated complex consumer voltages in a datastructure indexed by secondary distribution node, determining a voltagedifference between each of the voltage magnitudes corresponding to thecalculated complex consumer voltages stored in the data structureindexed by secondary distribution node and the voltage magnitude valuescorresponding to the voltage data for each of the metered consumernodes; identifying each voltage difference which exceeds a ratedmeasurement error of the corresponding meter as a voltage violation;determining a voltage difference range for each secondary distributionnode having voltage magnitudes corresponding to the calculated complexconsumer voltages stored in the data structure; and determining asecondary tap location based on the voltage difference range and numbervoltage violations for each secondary distribution node.
 16. The methodof claim 15 wherein determining the secondary tap location comprisesidentifying the secondary distribution node whose voltage difference isless than twice the rated measurement error and having the fewestvoltage violations as the secondary tap location.
 17. The method ofclaim 16 wherein determining the secondary tap location comprisesidentifying two secondary distribution nodes whose voltage differencesare less than twice the rated measurement error and having relativelylow numbers of voltage violations, and determining the secondary taplocation to be between the identified two secondary distribution nodes.18. The method of claim 17 comprising determining a cumulative voltagedifference for each of the identified two secondary distribution nodesand further narrowing the secondary tap location based on a relationbetween the cumulative voltage differences.
 19. The method of claim 1wherein obtaining the substantially simultaneous instantaneous real andreactive load data for the consumer nodes comprises obtaining at leastone measurement corresponding to one of the consumer nodes andmultiplying the measurement by a bypass diversion factor correspondingto that consumer node.
 20. A system for identifying tap loads in anelectric utility power distribution inventory zone, the inventory zonecomprising a plurality of nodes including at least one metereddistribution node and at least two metered consumer nodes, the systemcomprising: a data store comprising a non-transitory computer readablemedium of the data store contains an admittance matrix modeling theelectrical admittance between the nodes of the inventory zone,substantially simultaneous instantaneous real and reactive load data foreach of the metered nodes of the inventory zone, and substantiallysimultaneous instantaneous voltage magnitude data for each of themetered nodes of the inventory zone; and a data processorcommunicatively coupled to the data store and configured to: obtain theadmittance matrix from the data store; obtain the substantiallysimultaneous instantaneous real and reactive load data from the datastore; obtain the substantially simultaneous instantaneous voltagemagnitude data from the data store; determine a voltage phase angle foreach of the consumer nodes that solve a first system of power flowequations for the inventory zone having known values corresponding tothe real and reactive load data for the consumer nodes and in which thedistribution node is treated as a slack node; determine real andreactive tap loads corresponding to select ones of the consumer nodesthat: solve a second system of power flow equations for the inventoryzone having known values corresponding to the real and reactive loaddata for each of the nodes, voltage magnitude values corresponding tothe voltage data for each of the metered nodes, and having slackvariables representing the real and reactive tap loads, and minimize anobjective function whose value is positively related to at least one ofthe slack variables representing the real and reactive tap loads usingan iterative numerical solution technique wherein variables in thesecond system of power flow equations corresponding to the voltage phaseangles of the select ones of the consumer nodes are initialized tovalues corresponding to the corresponding determined voltage phaseangles that solve the first system of power flow equations; and generatea record in a non-transitory medium indicating the determined real andreactive tap loads corresponding to the select ones of the consumernodes.